Just tested my IP phone a few minutes ago and it's WORKING. Just like that. So I went into my router config and confirmed that Verizon pushed a firmware upgrade a few weeks ago. I guess that explains it. Despite their denials, the problem was due to something in the previous firmware version.
Update -- a few weeks ago my IP Communicator started working again. Just like that. I went into my router settings and confirmed that a firmware upgrade was pushed right before the software started working again. I'd say that confirms that the previous version of the router firmware was blocking packets, despite Verizon insisting they weren't blocking anything.